Maybe it's me. Or maybe my reed.
But whenever I play a low C or low Db, the tone sounds like it's vibrating. Or wavering, might I add. Okay, it sounds like there's water in the oboe or something, when there isn't any!
Why does this happen?

Make sure you are covering all the holes on the keys. Even a little bit of leakage could cause this problem. Also be sure your reed is open enough. Squeeze gently from the sides. And drop your jaw for the low notes.

Maybe you should take your oboe to a repair shop and have them check the pads on the keys. One of them might have a tear or could be loose. Hope this helps!
Oboegirl

<Added>

Also, try a different reed and see if it makes a difference. If it does, then you just have a bad reed.

I had this problem too a month ago. The most probable thing that happened will be that your Eb key hole is loose. Press the hole cover to see it is loose. If it is, tighten the screw on part that pushes the key hole open. If not, you better search for a professional to do that.

Have you checked the airtightness of the upper body of your oboe? Emission problems with low notes are quite offen related to (very) small air leaks in this region (or even small crack(hope it's not the case!!))

Make sure your oboe is at a nice 45 degree angle when you play your low range. I had this problem last year, and a similar post described the issue as being a lose Eb key. That was similar for me too. Try seeing if that's loose.